Volume of Tetrahedron given Surface to Volume Ratio Calculator

✖The Surface to Volume Ratio of Tetrahedron is the numerical ratio of the total surface area to the volume of the Tetrahedron.ⓘ Surface to Volume Ratio of Tetrahedron [R_A/V]

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✖Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.ⓘ Volume of Tetrahedron given Surface to Volume Ratio [V]

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Formula

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Volume of Tetrahedron given Surface to Volume Ratio

Formula

`"V" = (((6*sqrt(6))/"R"_{"A/V"})^3)/(6*sqrt(2))`

Example

`"110.8513m³"=(((6*sqrt(6))/"1.5m⁻¹")^3)/(6*sqrt(2))`

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Volume of Tetrahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2))
V = (((6*sqrt(6))/R_A/V)^3)/(6*sqrt(2))
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Volume of Tetrahedron - (Measured in Cubic Meter) - Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.
Surface to Volume Ratio of Tetrahedron - (Measured in 1 per Meter) - The Surface to Volume Ratio of Tetrahedron is the numerical ratio of the total surface area to the volume of the Tetrahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Tetrahedron: 1.5 1 per Meter --> 1.5 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (((6*sqrt(6))/R_A/V)^3)/(6*sqrt(2)) --> (((6*sqrt(6))/1.5)^3)/(6*sqrt(2))

Evaluating ... ...

V = 110.851251684408

STEP 3: Convert Result to Output's Unit

110.851251684408 Cubic Meter --> No Conversion Required

FINAL ANSWER

110.851251684408 ≈ 110.8513 Cubic Meter <-- Volume of Tetrahedron

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 8 Volume of Tetrahedron Calculators

Volume of Tetrahedron given Surface to Volume Ratio

Go Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron given Circumsphere Radius

Go Volume of Tetrahedron = ((2*sqrt(2/3)*Circumsphere Radius of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron given Total Surface Area

Go Volume of Tetrahedron = sqrt(2)/12*(Total Surface Area of Tetrahedron/sqrt(3))^(3/2)

Volume of Tetrahedron given Midsphere Radius

Go Volume of Tetrahedron = ((2*sqrt(2)*Midsphere Radius of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron given Insphere Radius

Go Volume of Tetrahedron = ((2*sqrt(6)*Insphere Radius of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron given Face Area

Go Volume of Tetrahedron = (((4*Face Area of Tetrahedron)/sqrt(3))^(3/2))/(6*sqrt(2))

Volume of Tetrahedron given Height

Go Volume of Tetrahedron = ((sqrt(3/2)*Height of Tetrahedron)^3)/(6*sqrt(2))

Volume of Tetrahedron

Go Volume of Tetrahedron = (Edge Length of Tetrahedron^3)/(6*sqrt(2))

Volume of Tetrahedron given Surface to Volume Ratio Formula

Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2))
V = (((6*sqrt(6))/R_A/V)^3)/(6*sqrt(2))

What is a Tetrahedron?

A Tetrahedron is a symmetric and closed three dimensional shape with 4 identical equilateral triangular faces. It is a Platonic solid, which has 4 faces, 4 vertices and 6 edges. At each vertex, three equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

How to Calculate Volume of Tetrahedron given Surface to Volume Ratio?

Volume of Tetrahedron given Surface to Volume Ratio calculator uses Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2)) to calculate the Volume of Tetrahedron, The Volume of Tetrahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Tetrahedron, and calculated using the surface to volume ratio of the Tetrahedron. Volume of Tetrahedron is denoted by V symbol.

How to calculate Volume of Tetrahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Volume of Tetrahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Tetrahedron (R_A/V) and hit the calculate button. Here is how the Volume of Tetrahedron given Surface to Volume Ratio calculation can be explained with given input values -> 110.8513 = (((6*sqrt(6))/1.5)^3)/(6*sqrt(2)).

FAQ

What is Volume of Tetrahedron given Surface to Volume Ratio?

The Volume of Tetrahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Tetrahedron, and calculated using the surface to volume ratio of the Tetrahedron and is represented as V = (((6*sqrt(6))/R_A/V)^3)/(6*sqrt(2)) or Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2)). The Surface to Volume Ratio of Tetrahedron is the numerical ratio of the total surface area to the volume of the Tetrahedron.

How to calculate Volume of Tetrahedron given Surface to Volume Ratio?

The Volume of Tetrahedron given Surface to Volume Ratio formula is defined as the total quantity of three dimensional space enclosed by the surface of the Tetrahedron, and calculated using the surface to volume ratio of the Tetrahedron is calculated using Volume of Tetrahedron = (((6*sqrt(6))/Surface to Volume Ratio of Tetrahedron)^3)/(6*sqrt(2)). To calculate Volume of Tetrahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Tetrahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Tetrahedron and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Tetrahedron?

In this formula, Volume of Tetrahedron uses Surface to Volume Ratio of Tetrahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

Volume of Tetrahedron = (Edge Length of Tetrahedron^3)/(6*sqrt(2))
Volume of Tetrahedron = sqrt(2)/12*(Total Surface Area of Tetrahedron/sqrt(3))^(3/2)
Volume of Tetrahedron = ((2*sqrt(2/3)*Circumsphere Radius of Tetrahedron)^3)/(6*sqrt(2))
Volume of Tetrahedron = ((2*sqrt(2)*Midsphere Radius of Tetrahedron)^3)/(6*sqrt(2))
Volume of Tetrahedron = ((2*sqrt(6)*Insphere Radius of Tetrahedron)^3)/(6*sqrt(2))
Volume of Tetrahedron = ((sqrt(3/2)*Height of Tetrahedron)^3)/(6*sqrt(2))
Volume of Tetrahedron = (((4*Face Area of Tetrahedron)/sqrt(3))^(3/2))/(6*sqrt(2))

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